Aerospace Simulations in C++

C.1 Introduction

The simulation examples of this book are provided on the CADAC CD-ROM in FORTRAN. This computer language has had a long and illustrious tradition in the engineering sciences. I did all coding starting in the mid 1960s in FORTRAN II, IV, and 77, until the year 2000, when a cadet from the U. S. Air Force Academy convinced me to give C++ a try. After some exploration I set out to upgrade CADAC to C++. It is not a straight conversion, but rather a complete re-write of the executive, modules, and utility functions, taking full advantage of the language’s polymorphism, inheritance, and encapsulation.

Today, CADAC++ as it is called is a mature trajectory simulation in ANSI/ISO 1998 C++. While teaching graduate courses at the University of Florida in modeling and simulation (M&S), I developed three self-study CD-ROMs that complement this textbook with C++ simulations. The first one, entitled “Building Aerospace Simulations in C++,”1 focuses on the architecture of the simulation framework, and uses simple cruise missile and satellite models to illustrate the interplay be­tween the executive and vehicle functions. The second CD lays the foundation for high fidelity simulations and is entitled "Fundamentals of Six Degrees of Freedom Aerospace Simulation and Analysis in FORTRAN and C++."2 As the title implies it juxtaposes FORTRAN with C++ by dealing with missile and aircraft simulations side by side. At the advanced level, the third CD, entitled “Advance Six Degrees of Freedom Aerospace Simulation and Analysis in C++.”3 treats some of the most dif­ficult topics of aerospace vehicle components like modeling of the elliptical Earth, inertial navigation systems, Kalman filters, global positioning systems (GPS), star trackers, and endo – and exo-atmospheric guidance laws. These three progressively more challenging CDs, this textbook, the CADAC Studio plotting programs, and the solutions manual,4 constitute a complete set of instructions for aerospace ve­hicle modeling and simulation. A more detailed description of each CD follows, with particular emphasis on their computer simulations.

C.2 C++ Architecture and Three-DoF Cruise Missile Simulation

The first CD, “Building Aerospace Simulations in C++,” introduces the appli­cation of C++. It assumes that you have taken a C++ language course and have a good understanding of Chapter 8, “Three-Degrees-of-Freedom Simulation." The lesson plan of the 16 labs is given in Table C. l. The labs are grouped into five training units, of which numbers 2-5 lead to four simulations: satellite, target on the ground, cruise missile, and short-range air-to-air missile. The SRAAM6 is a teaser of things to come. It models a missile/target engagement in six DoF without providing much detail. It is left to CD no. 2 to pick up the story from there with more elaborate discussions.

Table C. l Lesson plan of CD-ROM no. 1 “Building Aerospace Simulations in C++” Training modules Lab no. Training units 1 Introduction 1 Welcome; C++ Overview 2 Satellite3 2 Satellite3 Simulation 3 Rocket Propulsion; Class: Variable 4 Apparent Forces; Output 3 Target3 5 Integration; Input 4 Cruise3 6 Aero; Tables; Cruise3 Simulation 7 Turbojet; Polymorphism 8 Autopilot; Overloading Operators 9 Plotting; CADAC Studio 10 Environment; Event Scheduling 11 Line Guidance; Multiple Objects 12 Intercept; Communication Bus 13 Terminal Guidance; Subscribing 14 Engagements; Satellite Targeting 15 Global Engagements; Cruise3S Sim 5 SRAAM6 16 Six-DoF Equations; SRAAM6 Sim

Each lab discusses an aerospace vehicle component and combines it with a particular C++ feature. The topics become progressively more difficult as the simulations are combined to grow to a full engagement model with cruise missiles attacking ground targets, guided by overhead satellites.

More detail is provided in Table C.2 with references to the sections of this book. To build up to the satellite simulation in Lab 3 we need to cover only two modules: “newton” and “propulsion.” The simulation is called Satellite3 and models a satellite orbiting the Earth with optional rocket propulsion to change its orbital parameters. The equations of motion are based on Newton’s law expressed in inertial coordinates.

In Labs 4 and 5 a simulation is built for targets moving on the surface of the Earth, which is called Target3. Here we are especially challenged by having to include Coriolis and centrifugal accelerations to the equations of motions for the vehicles to hug the surface.

The remaining labs, 5-14, build toward the three-DoF cruise missile simulation Cruise3. Such modules like aerodynamics, turbojet propulsion, guidance, control, and seekers are added to create a complete vehicle.

Finally, in Lab 15 all three types of vehicle objects are combined to build the engagement simulation Cruise3S, which consists of cruise missiles flying toward multiple targets while monitored by overhead satellites. The trajectories of these engagements can be displayed by the plot programs of CADAC Studio from the CADAC CD.

C.3 High Fidelity Missile and Aircraft Simulations

The second CD, “Fundamentals of Six Degrees of Freedom Aerospace Simu­lation and Analysis in FORTRAN and C++,” introduces high fidelity missile and

Table C.2 Simulation and language features of CD-ROM no. 1 Lab Theme Simulation feature C++ Feature Book 1 Introduction 3 DoF Overview C++ Overview Chap. 8 2 Satellite Module “Newton” Statements Arrays Sec. 8.1.1 3 Satellite with propulsion Rocket propulsion Class “Variable” Inheritance Sec. 8.2.4 4 Ground targets Module “force” Output to screen and to files Sec. 5.3.1 5 Multiple ground targets Integration Module utility fcts. Input from file Sec. 3.2.2 6 Missiles Module Structure “Table” Chap. 8 Aerodynamics “aerodynamics” Overloading Sec. 8.2.3 7 Turbojet propulsion Module “propulsion” Polymorphism Sec. 8.2.4.2 8 Autopilot Module “control” Matrix utilities Operator overloading Sec. 9.2.3 9 Plotting CADAC Studio Output plotting 10 Events Environment Flight phases Module “environment” Class “Event” Sec. 8.2.1 Sec. 8.2.2 11 Missiles and targets Line guidance Multiple objects Polymorphism Sec. 9.2.4.3 12 Communication Terminal miss Communication bus Prob. 2.9 13 Terminal homing Module “seeker” Module “guidance” Subscribing of variables Sec. 9.2.5 Sec. 9.2.4 14 Multiple engagements Module “targeting” Overhead satellites Structure “Targeting” 15 Global engagements Missiles, targets, and satellites Satellite object 16 Air-to-air engagements Six-DoF Simulation Equations of motion Chap. 10

aircraft simulations in C++. It does this from a FORTRAN vantage point, based on simulations from the CADAC CD. The FORTRAN modules are converted to C++ and incorporated into the CADAC++ architecture of CD no. 1. A particular appeal of CD no. 2 is the dual language track. You can work either in FORTRAN, C++ or both.

Table C.3 provides an overview. Five training modules encompass 13 labs. As you can see, the emphasis is on modeling the components of aerospace vehicles. Because this CD focuses on aircraft and missiles, the Earth can be assumed to be quasiflat, as discussed in Sec. 3.2.2.7, and it can serve as an inertial reference frame. The individual training units have similar titles as those of CD no. 1, but are more elaborate, because of their high fidelity, six-DoF characteristics.

Table C.3 Lesson plan of CD-ROM no. 2 “Fundamentals of Six Degrees of Freedom Aerospace Simulation and Analysis in FORTRAN and C++” Training modules Lab no. Training units 1 Overview 1 Concepts in Modeling and Simulation 2 Primer of FORTRAN and C++ Simulations 2 Dynamics 3 Matrices, Vectors, and Tensors 4 Coordinate Systems 5 Kinematics 6 Equations of Motion; Numerical Integration 3 Aerodynamics & Propulsion 7 Aerodynamics; Table Look-up 8 Propulsion & Actuators 4 Guidance & Control 9 Autopilot 10 Seeker 11 Guidance 5 Performance 12 Performance Analysis 13 Summary Simulations Air-to-Air Missile in FORTRAN Air-to-Air Missile in C++ FI6 Aircraft in FORTRAN F16 Aircraft in C++

The detailed simulation buildup is shown in Table C.4. Both the air intercept missile (AIM) and the Falcon aircraft (FI6) are modeled in FORTRAN (FTN) and in C++. To jump-start your involvement, the primer of Lab 2 helps you, without going into details, to execute and plot the complete missile simulation in FORTRAN and C++. In Lab 3 the computational methods are discussed. Though up to this point the missile is used as illustration, the aircraft follows similar patterns. However, starting with coordinate systems in Lab 4, the aircraft requires separate treatment from the missile. As you proceed, you focus on one module at a time, skipping the nonexistent aircraft seeker module. Eventually in Lab 12 you evaluate the performance of the complete missile and aircraft using the final simulations. In a separate folder you are given the beginning simulations, code additions, and the final completed simulations.

This self-study course touches on all major elements of missile and aircraft sim­ulations in a FORTRAN and C++ environment. Because of the modular structure, you can expand and tailor the simulations to your own needs. If you want to model a cruise missile or unmanned air vehicle you would start with the FI6 simulation and import the seeker module from the missile simulation. You need not worry about violating copyright laws. All source code on the CDs is in the public domain; only the accompanying training charts are restricted by AIAA copyright.

Though this CD is complete in itself, it only deals with the fundamentals of six-DoF simulations. Advanced subjects, like elliptical Earth, inertial navigation systems, GPS, Kalman filters, and exo-atmospheric guidance are reserved for the third CD. Yet, you should first master the fundamentals before approaching these advanced subjects.

Table C.4 Creating aircraft and missile simulations in FORTRAN and C++ of CD-ROM no. 2 Simulations Training Aim Missile F16 Aircraft Lab no. Training units FTN C++ FTN C++ modules Startup 1 Overview 1 Introduction: Concepts in Modeling and Simulation 2 Primer AIMF02 AIMC02 2 Dynamics 3 Matrices, Vectors, and Tensors AIMF03 AIMC03 4 Coordinate Systems AIMF04 AIMC04 F16F04 F16C04 5 Kinematics AIMF05 AIMC05 F16F05 F16C05 6 Equations of Motion; Numerical Integration AIMF06 AIMC06 F16F06 F16C06 3 Aerodynamics & Propulsion 7 Aerodynamics AIMF07 AIMC07 F16F07 F16C07 8 Propulsion & Actuators AIMF08 AIMC08 F16F08 F16C08 4 Guidance 9 Autopilot AIMF09 AIMC09 F16F09 F16C09 & Control 10 Seeker AIMF10 AIMC10 11 Guidance AIMF11 AIMC11 F16F11 F16C11 5 Performance 12 Performance Analysis AIMF12 AIMC12 F16F12 F16C12 13 Summary Simulations Begin Sims AIMF# AIMC# F16F# F16C# Code Results AIMF% AIMC% F16F% F16C% Final Sims AIMFS AIMCS F16F$ F16C$

C.4 Advanced Components of Ascent Vehicles

The third CD, “Advanced Six Degrees of Freedom Aerospace Simulation and Analysis in C++,” presents advanced topics and assumes that you already have a good working knowledge of aerospace simulations, commensurate with CDs 1 and 2. It uses as a prototype a three-stage ascent vehicle, composed of a hypersonic air breather, exo-atmospheric transfer vehicle, and terminal interceptor.

Table C.5 outlines the 12 labs divided into seven training modules. Each lab consists of a training unit that introduces the subject and hands-on exercises using a self-contained simulation. There are 16 simulations, starting with simple or­bital trajectories over the elliptical Earth; a hypersonic vehicle with aerodynamics, propulsion, flight controller, inertial navigation, GPS and star tracker; a trans­fer vehicle; and finally an interceptor. Together they produce the full-up HYPER

Table C.5 Creating a three-stage ascent vehicle simulation with CD-ROM no. 3 “Advanced Six Degrees of Freedom Aerospace Simulation and Analysis in C++” Training modules Lab no. Training units Hands-on Simulation 1 Overview 1 2 Introduction; C++ Essentials CADAC Primer; Architecture Paper HYPER Slide Show 2 Elliptical Earth 3 Translational Equations HandsOn03 HYPER03 4 Attitude Equations HandsOn04 HYPER04 3 Hypersonic 5 Aerodynamics HandsOn05 HYPER05 Vehicle 6 Propulsion & Actuators HandsOn06 HYPER06 7 Flight Control HandsOn07 HYPER07 8 Monte Carlo & Turbulence HandsOn08 HYPER08 9 Inertial Navigation HandsOn09 HYPER09 10 Endo-Guidance HandsOnlO HYPER10 11 Global Positioning System HandsOnl 1 HYPER 11 12 Kalman Filter HandsOnl2 HYPER 12 13 Star Tracker HandsOnl 3 HYPER 13 4 Transfer Vehicle 14 Reaction Control HandsOnl4 HYPER 14 15 Orbit Insertion HandsOnl 5 HYPER 15 5 Aux Vehicles 16 Satellite & Radar HandsOnl 6 HYPER 16 6 Interceptor 17 Rendezvous HandsOnl7 HYPER 17 18 Intercept with Seeker HandsOnl8 HYPER 18 7 Performance 19 End-to-End Analysis HandsOnl 9 HYPER 20 Summary

simulation, which consists of three objects: ascent vehicle, satellite, and ground radar. All of them interact with each other and can be multiply instantiated.

The course starts with a review of C++ features and an in-depth discussion of the CADAC architecture. Then, at once, you will execute the complete HYPER simulation in a typical scenario. This should motivate you for the arduous task of building up to the HYPER simulation in 16 labs until in Lab 19 you conduct a complete end-to-end analysis.

Modeling and simulation can only be learned by doing. It requires a great investment of time and resources. The top experts in industry, academia, and government have made mastery of this subject a life-long quest. They combine a broad system engineering knowledge with mathematical modeling skills and computer savvy. Often they are the highest paid, nonsupervisory engineers.

To achieve this expertise in aerospace simulations you should build on a multidis­cipline college education in mathematics, flight mechanics, aerodynamics, propul­sion, and guidance and control, followed by hands-on training with prototype simulations. Having taught M&S courses for many years, I distilled them into these three CDs. They combine instructions and experimentation with a host of typical aerospace simulations. Everything you need is provided, you only supply the compiler. The one thing I cannot provide is the motivation it takes to plow through the material. That only can come from your commitment to and fondness for aerospace engineering.

References

‘Zipfel, P. H., “Building Aerospace Simulations in C++,” AIAA Self Study Series CD – ROM, 2003.

2Zipfel, P. H., “Fundamentals of Six Degrees of Freedom Aerospace Simulation and Analysis in FORTRAN and C++,” AIAA Self Study Series CD-ROM, 2004.

’Zipfel, P. H., “Advanced Six Degrees of Freedom Aerospace Simulation and Analysis in C++,” AIAA Self Study Series CD-ROM, 2005.

4Zipfel, P. H., “Solution Manual for Modeling and Simulation of Aerospace Vehicles,” AIAA 2000 (instructors can request a free copy from AIAA).

Appendix D